Interplay of dynamical and explicit chiral symmetry breaking effects on a quark

Abstract

The relative contributions of explicit and dynamical chiral symmetry breaking in QCD models of the quark-gap equation are studied in dependence of frequently employed ansätze for the dressed interaction and quark-gluon vertex. The explicit symmetry breaking contributions are defined by a constituent-quark sigma term whereas the combined effects of explicit and dynamical symmetry breaking are described by a Euclidean constituent-mass solution. We extend this study of the gap equation to a quark-gluon vertex beyond the Abelian approximation complemented with numerical gluon- and ghost-dressing functions from lattice QCD. We find that the ratio of the sigma term over the Euclidean mass is largely independent of nonperturbative interaction and vertex models for current-quark masses, $m_{u,d}(\mu )\le m(\mu )\le m_b(\mu )$, and equal contributions of explicit and dynamical chiral symmetry breaking occur at $m(\mu )\approx 400$~MeV. For massive solutions of the gap equation with lattice propagators this value decreases to about 200~MeV.

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